The entire segment this is part of makes it very clear they're looking for out-of-the-box thinking and a unique approach to problem solving in situations that might not be what they seem at first glance.

It starts with uncomfortable chairs and a written test on flimsy paper without desks; Smith's character noisily pulls over a table to write on while the military folks do the expected thing of struggling through. "You're everything we've come to expect from years of government training", they get told, and then their memories are wiped. Smith's character, instead, gets a briefing on the MIB and an intro to alien bugs pouring Kay some coffee.

(Said briefing also indicates Earth is a neutral zone for alien refugees. Again, "shoot first" is not what they want people doing!)

I watched the movie 2 times in past. I think Smith killing a child just because she is carrying science books (Oh she must be up to something) was sure out of the box and completely ridiculous as well. Also, how is Smith's characters action not "Shoot first"? please.